We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls.
Covering Lp Spaces by Balls / V.P. Fonf, M. Levin, C. Zanco. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 24:4(2014 Oct), pp. 1891-1897. [10.1007/s12220-013-9400-2]
Covering Lp Spaces by Balls
C. ZancoUltimo
2014
Abstract
We prove that, given any covering of any separable infinite-dimensional uniformly rotund and uniformly smooth Banach space $X$ by closed balls each of positive radius, some point exists in $X$ which belongs to infinitely many balls.
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